# Why the volume formula is the same for both a prism and for a cylinder?

## Why the volume formula is the same for both a prism and for a cylinder?

1 Answer. They are both similar in the way that the formula is base multiplied by height. They are different becasue of the type of shape on the base.

### What is the volume of the right prism?

To find the volume of a right prism, you multiply the length x width x height, or in the case of a right triangular prism, you find the area of the base and multiply this by the length or depth of the prism.

#### How is the volume of prism related to the volume of cylinder?

The cylinder and the prism have the same cross-sectional area, πr2, at every level and the same height. By Cavalieri’s Principle, the prism and the cylinder have the same volume. The volume of the prism is V = Bh = πr2h, so the volume of the cylinder is also V = Bh = πr2h.

**Can a cylinder and a rectangular prism have the same volume?**

A cylinder and a rectangular prism have the same volume and same height.

**What is the volume of the right cylinder?**

V = base area × height = πr2 × h = πr2h. By the above formula, we can say that the volume of a right circular cylinder is directly proportional to the square of its radius and also its height which means: If the radius of the base becomes double, then the volume becomes four times.

## What is the volume of cylinder?

π r² h

A cylinder’s volume is π r² h, and its surface area is 2π r h + 2π r².

### What is the volume of the cylinder?

V=πr2h

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h .

#### Do a cylinder and a rectangular prism with the same height have the same volume?

Do they have the same volume? Yes, due to Cavalieri’s principle. Even though these two cylinders are different, because they have the same height and base (and because every parallel cross section is congruent to the base), their volumes will be the same.